Questions tagged [optimization]
For questions concerning how to improve quantum computers on different aspects like performance, efficiency or fault-tolerance.
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Quantum AND† gate
In the paper Implementing Grover oracles for quantum key search on AES and LowMC, the authors use a different construction of AND gate and its adjoint rather than the Toffoli gate to decrease the T-...
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Techniques to parallelize controlled-unitaries controlled by the same qubit but acting on different target qubits
I need to find a way to parallelize a set of controlled-unitaries that are all controlled by the same qubit and are targetting $n$ different qubits. The main constraint that I have is that I can only ...
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T-depth in Qiskit
How to find T-depth in Qiskit? Is there any inbuilt function or some method to find T-depth? I know that the .depth() function exists which returns circuit depth (i....
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What is the original paper introducing the Variational Quantum Eigensolver?
My question is very simple. I am looking for original paper where Variational Quantum Eigensolver (VQE) has been introduced. After some Googling I was able to find many applications of VQE and its ...
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Cost of SWAP gate
We know that a SWAP gate needs three CNOT gates but I have seen papers which say that a SWAP gate can be achieved by necessary rewiring can are not counted towards the final quantum cost. I am ...
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Solving Hamiltonian eigenvalue problem
I would like to solve an eigenvalue problem of a Hamiltonian. I was able to find the lowest eigenvalue by converting the Hamiltonian into a matrix and applying linear algebra eigenvalue techniques. ...
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The energy levels crossover problem in Quantum Annealing
How to avoid energy levels crossover in quantum annealing by Kibble-Zurek mechanism? Any detailed references?
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The relationship between max-cut and max independent set
I know that Max Independent set problems are not equivalent to Mac-Cut problems. The cost function of Max-Cut can be described by the classical Ising model
$
H = \frac{1}{2} \sum_{i,j\in E}(1 - Z_i ...
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Qiskit: QAOAnsatz circuit with custom Hamiltonian
I am trying to implement the Quantum Approximate Optimization Ansatz by creating a parametrized subcircuit
$$V (α) = e^{−iH_M α_1} e^{−iH_D b_1} ... e^{−iH_M α_n} e^{−iH_D b_n}$$
with the custom ...
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Quantum Annealing vs Quantum Monte Carlo: can QMC do all that QA can?
I'm working on an essay about quantum technology, and the connection between the annealing algorithm and quantum computing hardware is an important transition in the text. I'd like to know if there is ...
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How linear combination of unitaries gradient work (Qiskit, PennyLane)?
I'm trying to implement linear combination of unitaries(LCU) gradient from Qiskit Gradient Framework
but on PennyLane.
First, i looked through the source code in Qiskit.
In Qiskit LCU gradient if we ...
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qutip.sesolve and qutip.optimize_pulse_unitary produce different results
I'm currently trying out some things with qutip in the field of optimal control (state-to-state transfer) and have some trouble to reproduce my results from the optimization process with sesolve.
My ...
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maximization of trace between two operators with respect to different norm constraints
I want to maximize $\text{Tr}(XY)$ over $X$ for fixed $Y$, where $X$ and $Y$ are both hermitian (but doesn't necessarily positive) operators, and $X$ is constrained by its p-norm bounded by $1$, i.e. $...
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Is No Free Lunch Theorem generalizable to Quantum Computation?
The "No Free Lunch Theorem" says: that when averaged across all possible problems, any two strategies have equivalent performance. However it uses Bayesian reasoning to arrive at this ...
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Closest quantum state with a fixed marginal: Analytical solution?
Let $\rho_{AB}$ be a bipartite state and let $\sigma_{B}$ be another state. What state $\tilde{\rho}_{AB}$ is closest to $\rho_{AB}$ and satisfies $\tilde{\rho}_B = \sigma_B$? We can define closeness ...
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Mathematical definition of QUBO problem
The quantum annealing approach is using the equivalence between QUBO matrix and Ising Hamiltonian to solve the problem. Therefore, it is necessary to transform a NP-hard problem into a QUBO matrix. ...
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Is the execution of a circuit neglectable for large optimization problems?
Assume a large combinatorial optimization problem should be solved (e.g. via Grover) and further assume there is a (near error free) universal quantum computer with a sufficient number of qubits (and ...
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Number of required Qubits for combinatorial optimization problems
In general, are there better ways to encode combinatorial optimization problems, e.g. TSP, than using O(n^2) Qubits and still find optimal solutions (with high ...
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Is it possible to use a quantum algorithm to optimize quantum chips
I'm really new to QC, so please excuse if this is a dumb question.
I was looking at the different Qubit configurations/arrangments in chips and was wondering if it is possible to create an algorithm ...
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Evaluating the derivative of a Quantum Circuit
After this post this weekend which got an excellent response, I've been trying to get into the solution that is given by the paper and applying it to my circuit. My original circuit is far bigger and ...
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How does qiskit's CircuitQNN calculate the gradients of circuits?
I'm trying to understand how the gradients are calculated for any given circuit using qiskits CircuitQNN and ...
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Can any binary problem be solved by a QUBO?
As far as I know, if a computing problem can be solved by the quantum annealing approach, it also means the solution space should be binary, e.g., a vector that only contains either 0 and 1. Otherwise,...
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Confusion about the objective function of VQEs and QAOAs
I am a bit puzzled on how the objective function of the VQEs and QAOAs. Of course, the parametrised state is constructed differently in these two algorithms but they do share a common objective to be ...
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Qiskit's classifier is not optimising the weights
I am using qiskit's VQC to build a classifier. Dimensionality of the data is 2 and number of classes are 4. The feature map I used is ZZFeatureMap and ansatz is the RealAplitudes. Then entanglement ...
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How to show mathematically the equivalency between Ising Model and QUBO?
It is said that the Ising Model using spin variables $s ∈ \{−1, 1\}$
$$H(s)=\sum_{i}h_is_i+\sum_{i<j}J_{ij}s_is_j,$$
and a Quadratic Unconstrained Binary Optimization (QUBO) problem with binary ...
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Enforcing a particular layout mapping in Qiskit
I would like to ask how to set a particular layout during transpiling. I guess that the layout can be set by the initial_layout parameter in the transpiler. However,...
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Save output, wavefunction file and orbital information in Qiskit
I am going through LiH ground state energy calculation. I would like to know how to save the output file in Qiskit as one would do in classical computing using software like Gaussian or Psi4.
Also, ...
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Example of lower bound on spectral gap for adiabatic quantum computing
is there a list of reference for which the authors prove a lower bound of the spectral gap for an adiabatic quantum algorithm? I.e. I am searching for examples where the authors solve a problem with ...
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How can a Mixer Hamiltonian restrict the search within a subspace of the statespace in QAOA?
I understand that the role of the Mixer Hamiltonian prevents the creation of a constant function where there is nothing to be minimized.
I would like to understand from a mathematical perspective how ...
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QAOA for Binary Optimization
I have reduced an optimization problem to a Binary Integer Linear Programming model as follows:
$$\sum_{j=1}^{2^n-1} f(C_j)x_j \rightarrow \max$$
$$\text{subject to} \sum_{j=1}^{2^n-1} S_{i,j}x_j=1\,\,...
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Initial state for QAOA
I'm learning about QAOA and I got curious about how they choose initial state. They somehow decided to choose initial state as equal superposition of all possible state and I wonder that there is any ...
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Pack Header Error when using QAOAProgram [closed]
I want to use QAOAProgram from Qiskit in the following way:
...
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What type of tasks it is possible to solve on a quantum simulator?
In this article, the author claimed that researches from Harvard and MIT created 256 qubits quantum simulator. However, we are not talking about piece of software on a classical computer but actual ...
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Complexity of $n$-Toffoli with phase difference
I'm interested in the $n$-Toffoli gates with phase differences. I found a quadratic technique in section 7.2 of this paper.
Here's the front page of the paper.
Here's an image of the section that I'm ...
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Solving linear system $Ax=b$ with exponential speed-up via binary optimization?
The main disadvantage of HHL algorithm for solving $A|x\rangle = |b\rangle$ is that exponential speed-up is reached only in case we are interested in value $\langle x|M|x\rangle$, where $M$ is a ...
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How to improve embedding process in D-Wave?
I am quite new to the quantum computing field.
Currently, I am trying to solve a combinatorial optimization problem on a D-Wave system, which I successfully translated into QUBO form. I also managed ...
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Minmax theorem for optimization over isometries and states
I have the following minmax problem and I am wondering if the order of the minimum and maximum can be interchanged and if yes, why?
Let $\|\cdot\|_1$ be the trace norm defined as $\|\rho\|_1 = \text{...
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Quantum annealing - studies showing empirical evidence for better performance in comparison with classical computers
Currently, it is not known wheter quantum anneling or algorithms like VQE and QAOA for general purpose quantum computers bring about any increase in computational power. However, there are some ...
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What explains my anomalously scaled up VQE?
I am trying to implement VQE from the Qiskit to obtain the ground state of a very specific Hamiltonian that has been generated via a docplex minimized quadratic ...
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Measurement on a specific basis and proof of circuit output
I am trying to understand a proof from Practical optimization for hybrid quantum-classical algorithms. In particular, I need clarifications on how do you perform the measurement on a different basis ...
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QAOA not returning solution for simple clustering problem
I am following University's of toronto QML course and there's a section where QAOA is applied to cluster a set of vectors by mapping the clustering problem into a Maxcut problem. Unfortunately qiskit'...
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Role of entanglement in a VQE ansatz for combinatorial problems
Variational Quantum Eigensolver is used in quantum chemistry and combinatorial optimization (CO). I'm interested in the latter. In the CO setting a Hamiltonian is a diagonal matrix with real entries ...
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What's the role of mixer in QAOA?
In QAOA algorithm, two terms are being discussed; 1) clause or cost (C) Hamiltonian and 2) mixer consisting of pauli X gates.
What is the role of this mixer? Not clear why it comes after the C. ...
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Set the bounds for ansatz parameters in VQE
How can I make intervals for free parameters when I use VQE function? (https://qiskit.org/documentation/stubs/qiskit.algorithms.VQE.html)
I have built a parametrized ($\theta_1,...,\theta_n$) circuit ...
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Qiskit Portfolio Optimization : Does the resulting matrix show the stock combination to select?
The IBM Qiskit Portfolio Optimization sample finally provides an array similar to [1,0,1,1] representing the 4 digits as the stocks. So does the ...
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Is there a general proof of convergence of variational quantum eigensolvers (VQEs) to the minimum eigenvalue?
For QAOA it is known that in the large $p$ limit, the algorithm finds the minimum/maximum (see article A Quantum Approximate Optimization Algorithm).
Is there in general a proof for VQE starting ...
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What exactly happening in QAOA in a general way?
So I know that in QAOA we have the two hamiltonians. Mixer and Cost Hamiltonian.
Lets start:
First we have our Qubits which get in the Superposition if we add the Hadamard Gate.
Then we have the both ...
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In quantum adiabatic simulation, is the $s$ in $(1-\frac{s}{T})H_{in}+\frac{s}{T} H_{cl}$ related to the $t$ in $e^{-iHt}$?
I just want to do a whole adiabatic calculation on quantum circuit.
To prepare two Hamiltonian of $H_{initial}$ and $H_{classical}$ and solve $H_{classical}$ using adiabatic calc like quantum ...
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From QUBO matrix to Ising model in Qiskit
Given a general QUBO matrix $Q$ for a quadratic minimization problem, is there a Qiskit way to obtain the Pauli gate list or the Ising model for it? A related question is Qiskit: Taking a QUBO matrix ...
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